The Parker–Sochacki method for solving systems of ordinary differential equations using graphics processors

In this paper we describe the Parker–Sochacki method, which is used for solving systems of ordinary differential equations and the implementation of this method on the graphics processors. As a test, we consider the solution of the classical $N$ bodies problem. The algorithm makes possible to effectively use massive parallel graphics processors, and provides an acceptable accuracy at a multiple time reduction as compared to the processors of a conventional architecture.